The product  of   rn-paracompact and   rn-strongly  paracompact are briefly disc. ussed.

Despite ample research on soft linear spaces, there are many other concepts that can be studied. We introduced in this paper several new concepts related to the soft operators, such as the invertible operator.  We investigated some properties of this kind of operators and defined the spectrum of soft linear operator along with a number of concepts related with this definition; the concepts of eigenvalue, eigenvector, eigenspace are defined. Finally the spectrum of the soft linear operator was divided into three disjoint parts.

     In this work, we present new types of compact and Lindelöf spaces and  some facts and results related to them. There are also types of compact and Lindelöf functions and the relationship between them has been investigated. Further, we have present some properties and results related to them.

A random laser is a non-conventional laser whose feedback mechanism is based on dissorder-induced light. However, random lasers occur in gain media with numerous scatterers and produce coherent laser emission without any predesigned cavity. The generation of coherent emission from multiple scattering is quite general and its basic principles are shown here using sulforhodamine B-TiO suspensions system. These suspensions were pumped with 337.1 nm pulses from N2 laser and the spectral and temporal behavior of light emitted from the pumped surface was recorded. When we pump power above a certain threshold a dramatic narrowing of the emission line width and a shortening of the emitted pulses were observed. We have experimentally found that i

In This paper generalized spline method and Caputo differential operator is applied to solve linear fractional integro-differential equations of the second kind. Comparison of the applied method with exact solutions reveals that the method is tremendously effective.

The current research aims to measure Generalized Anxiety Disorder among students of the University of Sulaymaniyah / College of Basic Education, and to identify the significance of differences between sex, scientific specialization and age, and for that reason, the research sample of (102) male and female students was chosen in a random manner, and the researcher used the diagnostic criteria for the generalized anxiety disorder contained He mentioned it in the Statistical and Diagnostic Manual of Psychiatry, and the paragraphs of the scale were formulated according to those standards after they verify the conditions of honesty and consistency, and the use of appropriate statistical means. The results of the research indicated that genera